This is just hilarious and I am not sure for how long the Watson 2016 Foundation site will be allowed to stay online (no affiliation with IBM whatsoever). We all know how screwed-up the american election is so this is even more fun when you see it as an outsider.
But lets play with the idea of having Watson as the President of the United States, just for fun.
Watson would probably do a better job than all the candidates in the current election, but he has a few disadvantages, he does not make decisions in the way you would expect from a President, he provides suggestions to decision and evidence that support them. Letting him decide on how to negotiate with China or Syria would probably not be the best thing, or letting him manage the talks with Putin or keeping it all in order in the UN security counsel. He will need a lot of support and he needs to be trained. He could definitely provide the insight and information that should be communicated. The training could probably be safe-guarded in one way or the other, but he would need a high quality translator / rethoric-professional (aka a personal Karl Rowe) that could convey his suggestions and his information in a way that does not make friends and foos of USA go bananas.
What Watson really could do in the governments all over the world is to make them more efficient in many ways and also make sure that decisions are made based on facts and that things are not missed. People cannot remember everything, Watson can.
Watson would make it much easier for the politcians to make the right decisions based on the right information.
Since he is extremely good at unstructured data (hello all these documents) and to read fast, he can probably bring out some of that dead-meat that is often present in governmental organisations all over the world. He would also provide a sincere and fully transparent politics, which I guess would be highly appreciated in a country like US with all the lobby, Super PACS and large corporation influence.
I think the Watson for President initiative is very interesting and is pushing the thought a bit, regardless if it is a sincere initiative or just for fun.